Constrained OCO algorithms have applications in advertising with budget constraints, control of capacitated communication systems, queuing problems [1]}, etc. Nevertheless, they are notoriously hard to tackle. In particular, [2]} showed that no algorithm can achieve sublinear regret and constraint violation relative to each benchmark:
\(x^\star \in \mathcal {X}_T^{\text{max}}=\Big \lbrace x\in \mathcal {X}\, \Big \vert \, \textstyle \sum _{t=1}^T g_t(x)\preceq 0 \Big \rbrace . \) 
